Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Reason about standard deviation without calculating
Statistics and probability
CCSS HSS.ID.A.2CCSS HSS.ID.A.3England: GCSE Higher Statistics
Objective and success criteria
Students will: Reason about standard deviation without calculating.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Spread: standard deviation
Leads to: the next skill in this area.
Materials: Squared paper for charts, Class survey data, Sticky notes for a live chart, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Spread: standard deviation). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find the population standard deviation of: 5, 9, 5, 9 → 2Prompt: Find the mean, then each value's distance from it.
- Set A: 24, 25, 25, 26, 25. Set B: 17, 22, 25, 28, 33. Which set has the larger standard deviation? (A / B / They are equal) → BPrompt: Standard deviation measures how spread out the data are from the mean.
- Find the population standard deviation of: 8, 16 → 4Prompt: Find the mean, then each value's distance from it.
Hook · 5 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Reason about standard deviation without calculating. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Set X: 34, 36, 38, 40, 42 Set Y: 22, 30, 38, 46, 54 Both have mean 38. Which set has the larger standard deviation?
- Step 1: Y
- Answer: Y
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Set X: 54, 55, 56, 57, 58 Set Y: 48, 52, 56, 60, 64 Both have mean 56. Which set has the larger standard deviation? (X / Y / They are equal) → YPrompt: Standard deviation measures how far values are from the mean.
- Some lengths have standard deviation 3 cm. Every length is multiplied by 5. What is the new standard deviation, in cm? → 15Prompt: Adding the same amount shifts all values but keeps the gaps.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Set X: 21, 24, 27, 30, 33 Set Y: 5, 16, 27, 38, 49 Both have mean 27. Which set has the larger standard deviation? (X / Y / They are equal) → YPrompt: Standard deviation measures how far values are from the mean.
- A set of test scores has standard deviation 12. The teacher adds 16 bonus points to every score. What is the new standard deviation? → 12Prompt: Adding the same amount shifts all values but keeps the gaps.
Watch out for
- Forgetting to put data in order before finding the median.
- Reading a bar's height wrongly when the scale goes up in 2s or 5s.
Support and stretch
Support
- Review first: Spread: standard deviation.
- Use concrete materials: squared paper for charts.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-10.
Free lesson plan from eurekami.com/lesson-plan-builder